Подход к параметризации движений в

!
.
,$
%
.!
-
,
.#
:
%
.
:
'
,%
,
&
,
.
(
,
,
,
.)
(
,
,
&
&
,&
&
. *
(
,
.
'
,
,
&
[1]. '
,
,
,
&
&
.
'
&
&
&
,
,
&
&
,
%
&
..
&
.)
&
.'
.
( &
:
Character = <Skeleton, MuscleSystem>
/
Skeleton –
MuscleSystem –
;
( &
.
'
(
)
Skeleton = <{RigidBody}, {Joint}>,
RigidBody –
Joint –
.
'
(
) [2]:
;
&
,
t–
p(t) –
p'(t) –
p''(t) –
u(t) –
,
:
Joint = <p(t), p'(t), p''(t), u(t)>,
;
;
;
;
.
'
&
,
Xbase –
SupportPoint –
,
& ,
& :
CharacterState(t) = <Xbase, {p(t)}, {SupportPoint}>,
–
,
;
( "
&
,&
"
,
&
&
:
-
.
#
-
<
StatePair = <t, p(t)>.
%
,
,
,
&
BasicMovement(t, CharacterState(t), {Param}) = {StatePair},
,
,
,
&
&
. = &
,
,
,
Param –
=
(
&
,
:
&
.
&
,
&
-
.
#
%
&
.#
[3]
.
(
[4]. '
,
-
,
( :
MuscleSystem = {MusclePair},
MusclePair = <JointRf, dofNum, PosMuscle, NegMuscle>,
MusclePair –
( &
JointRf –
dofNum –
PosMuscle = Muscle –
NegMuscle = Muscle –
Muscle –
( .
;
(
;
;
( ;
( ;
t,
(
,
,
p''(t),
&
–
&
&
.@
( ,
,
.
A (
StrainSpd(t) –
Strain(t) [0, 1] –
VFC(p') –
%%
StrainF(p) –
RelaxF(p) –
,
,
,
Muscle = <StrainSpd(t), Strain(t), VFC(p'), StrainF(p), RelaxF(p)>,
( ;
( ;
(
,
(
;
(
.
(
t
%
:
,
#
:
;
RealF(t) = AM.StraintF(p(t)) AM.Strain(t) AM.VFC(p'(t)) + PM.RelaxF(t),
(
;
(
.
,
&
( &
(
(
),
.=
&
&
&
).
&
,
AM –
PM –
#
u(t),
–
%%
(
(
#
,
F &
&
1)
2)
-
&
(
&
&
&
,
..
,
%
.#
&
,
-
:
–
(
/
,
&
&
3)
,
Condition = f(t, CharacterState(t), {Param}) (True, False).
,
&
–
.'
& ;
&
&
:
;
( (
.
)
,
:
%
-
..
-
&
&
,
&
&
,
,
:
CompoundMovement = <{Param}, {(BasicMovement)}>.
(
&
&
(
)
=
,
,
&
&
.F
,
&
&
&
&
.
. = -
,
,
.#
,
–
&
H
&
&
,
&
,
,
,
&
,
,
,
.H
(
. &
&
&
:
–
,
,
&
2)
;
–
3)
&
;
&
–
&
=
-
&
&
4)
-
.
)
1)
-
&
&
&
&
(
&
,
,
&
-
;
&
–
,
,
&
&
,
,
I
-
.
,
&
,
. )
,
.
& ,
- &
( &
&
&
)
&
-
&
(
-
&
). #
.
=
.#
,
,
,
I
.#
&
& ,
,
,
&
.<
&
(
,
&
.
J
&
&
.
& ,
,
&'()*+,-(./01 345+*/56
&
,
&-
&
&
.<
&
,
& (
H
.
(
.@
,
.!
&
:
,
.
,
,
(
I
,
.=
,
&
I
,
'++
(dll). /
&
%
:
,
.
,
,
-
.
:
,
,
&
OpenGL
&
(
.=
%
).
I
.#
I
,
,
,
&
I
,
,
,
-
,
&
&
.'
–
.
,
% &
,
,
–
.
,
–
. =
&
=
.
&
,
.!
%
&
.@
(
.
,
&
<
,
&
,
&
.*
-
,
,
,
&
.H
-
,
&
.
1. David Sturman, The State of Computer Animation. – ACM SIGGRAPH Computer Graphics, Vol.32, No.1, February, 1998.
2. Larry Israel Gritz, Evolutionary controller synthesis for 3-D character animation. – dissertation, George Washington University, 1999.
3. D. Baraff, An Introduction To Physically Based Modeling. – SIGGRAPH Course Notes, ACM SIGGRAPH, 1995.
4. !. u
, H&
. – A.: A , 1988 ., 128 .
&'
A
'
&*
–
%
J'H*v *
u
<
&
v
.
E-mail: [email protected]
Abstract
This work presents an approach to representation of parametrical movement in computer aided character animation as a set of elementary parametrical units. Main principles of the approach is considered along with description of used character and movement models. A
character animation system based on the suggested approach is also briefly considered – its main functional mechanisms and capabilities
are described.